The club was a cricket club when it formed in 1820 as The Wednesday Cricket Club (named after the day of the week when they played their matches). A meeting on the evening of Wednesday 4 September 1867 at the Adelphi Hotel established a footballing side to keep the team together and fit during the winter months. They played their first match against The Mechanics on 19 October the same year.
Still, as football tattoos go, it is nowhere near as bad as some examples out there. Manchester City fans in particular seem to have a bad ink habit.
At least the only people who will know this is wrong is Sheffield Wednesday fans and even then, QED, they might not be totally sure when their club was formed.
EDIT: It appears it's a fake! Ha! Thought the tattooist had made a good job of making those 7s look really similar. I'll put this in my box of reasons to dislike Sheffield Wednesday along with the 1991 League Cup final and an ex-girlfriend hailing from the city.